Toán Lớp 11: Tìm gtnn , gtln
y=sinx – cosx +3
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Toán Lớp 11: Tìm gtnn , gtln
y=sinx – cosx +3
Mình đang gấp , cảm ơn ạ
Comments ( 1 )
y = \sin x – \cos x + 3\\
y = \sqrt 2 \sin \left( {x – \dfrac{\pi }{4}} \right) + 3\\
– 1 \le \sin \left( {x – \dfrac{\pi }{4}} \right) \le 1\\
\Rightarrow – \sqrt 2 \le \sqrt 2 \sin \left( {x – \dfrac{\pi }{4}} \right) \le \sqrt 2 \\
\Rightarrow 3 – \sqrt 2 \le y \le 3 + \sqrt 2 \\
\Rightarrow \left\{ \begin{array}{l}
\min y = 3 – \sqrt 2 \\
\max y = 3 + \sqrt 2
\end{array} \right.
\end{array}$